Browsing by Author "Petras, Ivo"

Now showing 1 - 6 of 6

Citation - WoS: 15
Citation - Scopus: 17
A Fractional Variational Approach to the Fractional Basset-Type Equation
(Pergamon-elsevier Science Ltd, 2013) Baleanu, Dumitru; Baleanu, Dumitru; Garra, Roberto; Petras, Ivo; 56389; Matematik
In this paper we discuss an application of fractional variational calculus to the Basset-type fractional equations. It is well known that the unsteady motion of a sphere immersed in a Stokes fluid is described by an integro-differential equation involving derivative of real order. Here we study the inverse problem, i.e. we consider the problem from a Lagrangian point of view in the framework of fractional variational calculus. In this way we find an application of fractional variational methods to a classical physical model, finding a Basset-type fractional equation starting from a Lagrangian depending on derivatives of fractional order.
Citation - WoS: 31
Citation - Scopus: 33
Fractional Bateman-Feshbach Tikochinsky Oscillator
(Iop Publishing Ltd, 2014) Baleanu, Dumitru; Baleanu, Dumitru; Asad, Jihad H.; Petras, Ivo; 56389; Matematik
In the last few years the numerical methods for solving the fractional differential equations started to be applied intensively to real world phenomena. Having these things in mind in this manuscript we focus on the fractional Lagrangian and Hamiltonian of the complex Bateman-Feshbach Tikochinsky oscillator. The numerical analysis of the corresponding fractional Euler-Lagrange equations is given within the Grunwald-Letnikov approach, which is power series expansion of the generating function.
Citation - WoS: 30
Citation - Scopus: 35
Fractional Pais-Uhlenbeck Oscillator
(Springer/plenum Publishers, 2012) Baleanu, Dumitru; Baleanu, Dumitru; Petras, Ivo; Asad, Jihad H.; Pilar Velasco, Maria; 56389; 56389; Matematik
In this paper we study the fractional Lagrangian of Pais-Uhlenbeck oscillator. We obtained the fractional Euler-Lagrangian equation of the system and then we studied the obtained Euler-Lagrangian equation numerically. The numerical study is based on the so-called Grunwald-Letnikov approach, which is power series expansion of the generating function (backward and forward difference) and it can be easy derived from the Grunwald-Letnikov definition of the fractional derivative. This approach is based on the fact, that Riemman-Liouville fractional derivative is equivalent to the Grunwald-Letnikov derivative for a wide class of the functions.
Citation - WoS: 33
Citation - Scopus: 35
Fractional-order two-electric pendulum
(Editura Acad Romane, 2012) Baleanu, Dumitru; Baleanu, Dumitru; Asad, Jihad H.; Petras, Ivo; Matematik
In this paper we study the fractional Lagrangian of the two-electric pendulum. We obtained the fractional Euler-Lagrangian equation of the system and then we studied the obtained Euler-Lagrangian equation analytically, and numerically. The numerical method used here is based on Grunwald-Letnikov definition of left and right fractional derivatives.
Citation - WoS: 4
Citation - Scopus: 4
Measurement of para-xylene diffusivity in zeolites and analyzing desorption curves using the mittag-leffler function
(Springernature, 2016) Zaman, Sharif F.; Baleanu, Dumitru; Baleanu, Dumitru; Petras, Ivo; Matematik
The new fractional calculus modeling based on Mittag-Leffler function has been employed to generate a better fit model to analyze the ZLC desorption curves for para-xylene diffusion in ZSM-5 zeolites. The diffusivity values generated herewith at 100, 125 and 150 degrees C are reported as 4.4 x 10(-13), 4.98 x 10(-13) and 5.2 x 10(-13) m(2)/s, respectively. The activation energy for this diffusion process is found 4.2 kJ/mol and diffusion proportional constant (D-0) is 1.85 x 10(-12) m(2)/s. The simplified model for ZLC response can be a better way to treat desorption data in ZLC experiments.
Citation - WoS: 19
Citation - Scopus: 20
Numerical solution of the fractional Euler-Lagrange's equations of a thin elastica model
(Springer, 2015) Baleanu, Dumitru; Baleanu, Dumitru; Asad, Jihad H.; Petras, Ivo; Matematik
In this manuscript, we investigated the fractional thin elastic system. We studied the obtained fractional Euler-Lagrange's equations of the system numerically. The numerical study is based on Grunwald-Letnikov approach, which is power series expansion of the generating function. We present an illustrative example of the proposed numerical model of the system.